I think both are grammatically correct, but they have slightly different meanings. If you asked me "What color do you like?", I would answer "Blue". But if you asked me what kind of colors do you like?", I would answer "Cool colors" (such as blue, purple, and green). Same with the animal sentences - "What animal do you like?" asks for a specific animal, while "What kind of animals do you like?" asks for a group or type of animals.